Optimal human papillomavirus vaccination strategies in the context of vaccine supply constraints in 100 countries

Summary Background Countries are recommended to immunise adolescent girls routinely with one or two doses of human papillomavirus (HPV) vaccines to eliminate cervical cancer as a public health problem. With most existing vaccine doses absorbed by countries (mostly high-income) with existing HPV vaccination programmes, limited supply has been left for new country introductions until 2022; many of those, low- and middle-income countries with higher mortality. Several vaccination strategies were considered by the Strategic Advisory Group of Experts on Immunization to allow more countries to introduce vaccination despite constrained supplies. Methods We examined the impact of nine strategies for allocating limited vaccine doses to 100 pre-introduction countries from 2020 to 2030. Two algorithms were used to optimise the total number of cancer deaths that can be averted worldwide by a limited number of doses (knapsack and decreasing order of country-specific mortality rates), and an unoptimised algorithm (decreasing order of Human Development Index) were used. Findings Routinely vaccinating 14-year-old girls with either one or two doses and switching to a routine 9-year-old programme when supply is no longer constrained could prevent the most cervical cancer deaths, regardless of allocation algorithm. The unoptimised allocation averts fewer deaths because it allocates first to higher-income countries, usually with lower cervical cancer mortality. Interpretation To optimise the deaths averted through vaccination when supply is limited, it is important to prioritise high-burden countries and vaccinating older girls first. Funding 10.13039/100004423WHO, 10.13039/100000865Bill & Melinda Gates Foundation.


Methods
Supplementary Figure 1.Countries that have not introduced a national HPV immunisation programme in 2020.Of the 100 countries that have yet to introduce a national HPV immunisation programme, 60 are lowand lower-middle income countries and 24 are upper-middle-income countries.The French overseas departments-French Guiana, Guadeloupe, Martinique, and Reunion-are classified as high-income economies.

Vaccination strategies
The WHO Strategic Advisory Group of Experts on Immunization considered several vaccination strategies which allowed more countries to introduce vaccination despite constrained supplies.Routine HPV vaccination programmes target girls between 9 and 14 years of age.In the first year of HPV vaccine introduction, countries may also implement multiple age-cohort (MAC) vaccinations, vaccinating older girls that routine programmes would miss.Available vaccines were distributed according to one of nine vaccination strategies, which cover strategies with and without multiple agecohort MAC or single-year catch-up, one-and two-dose and extended interval schedules, presented in Supplementary Table 1.

Vaccination strategy Description Routine 2 doses
Routine 2 doses no MAC 1 Routine: 9-year-old girls are given 2 doses every year Routine 2 doses with MAC 1 (2 doses) Routine: 9-year-old girls are given 2 doses every year MAC 1 : 10-14-year-old girls are given 2 doses in the first year Routine 2 doses with MAC 1 (1 dose) Routine: 9-year-old girls are given 2 doses every year MAC 1 : 10-14-year-old girls are given 1 dose in the first year Routine 1 dose Routine 1 dose no MAC 1 Routine: 9-year-old girls are given 1 dose every year Routine 1 dose with MAC 1 (1 dose) Routine: 9-year-old girls are given 1 dose every year MAC 1 : 10-14-year-old girls are given 1 dose in the first year Routine 14-year-old, later switch to routine 9-year-old (1-dose) Routine: 14-year-old girls are given 1 dose for the first ten years.In the sixth year when supply is no longer constrained, 9-year-old girls are given 1 dose every year Extended interval/vaccinating older girls

3-year extended interval
Routine: 9-year-old girls are given their first dose Extended interval: Three years later, the girls (now aged 12) are given their second dose 3-year extended interval + MAC 1 (1-dose) Routine: 9-year-old girls are given their first dose MAC 1 : 10-14-year-old girls are given 1 dose in the first year Extended interval: Three years later, the girls (now aged 12) are given their second dose Routine 14-year-old, later switch to routine 9-year-old Routine: 14-year-old girls are given 2 doses for the first ten years.In the sixth year when supply is no longer constrained, 9-year-old girls are given 2 doses every year 1

Optimised allocation with knapsack
To optimise the use of scarce vaccine doses, we examined the health impact of using knapsack for allocating doses between pre-introduction countries and nine vaccination strategies for allocating doses within-country populations.Here, we describe the knapsack algorithm adopted.
Which countries should be selected for country introduction in a particular year?Over the years 2020 to 2030, we want to allocate limited vaccine supplies to pre-introduction countries for their HPV vaccination programme.As of May 2020, 100 such countries have yet to introduce a national HPV immunisation programme (Supplementary Figure 1), and the vaccine demand of country  is  !" for year .If country  introduces HPV vaccination in year , it could prevent  !" cervical cancer deaths (or cases); the profit of selecting country .We assume that once countries have introduced HPV into their immunisation programme, they will implement an annual routine vaccination programme.To simplify the problem, we do not consider partial introductions, vaccine acceptance or preferences (e.g., based on valency or country of production), affordability of procurement and distribution costs, or programmatic feasibility of delivering vaccines.
Given the following parameters,  != the annual capacity, i.e., the number of vaccine doses available in year ,  != the number of pre-introduction countries in year ,  !" = the weight, vaccine demand of each country  in year , for  = 1, 2, . . .,  !,  !" = the value associated with country  in year , i.e., the deaths (or cases) that can be averted if country  introduces in year  and routinely vaccinated from year  onwards, for  = 1, 2, . . .,  ! .
Then, we formulate our 0-1 knapsack problem as: Maximise where  !# ,  !$ , … ,  !% take values 0 or 1, such that if  !" = 1, then county  is selected for introduction in year .We solve this single knapsack problem by using the dynamic programming approach in R (R Foundation for Statistical Computing).We performed optimised allocation (knapsack) for all nine vaccination strategies under different supply projections (5% reduction as base case, and 0% and 10% reduction as sensitivity analyses).